// Numbas version: exam_results_page_options {"name": "future value - simple interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "functions": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "useCustomName": false, "scripts": {}, "marks": 0, "sortAnswers": false, "customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "
$\\$\\,$[[0]] (to the nearest cent)
", "gaps": [{"unitTests": [], "maxValue": "S", "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the nearest cent.", "marks": 1, "allowFractions": false, "minValue": "S", "customName": "", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "useCustomName": false, "scripts": {}, "mustBeReducedPC": 0, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "strictPrecision": false, "precisionType": "dp", "precision": "2"}]}], "advice": "We are asked to find the future value using simple interest. Therefore we will use the equation
\n$S=P(1+rt)$,
\nwhere $S$ is the future value, $P$ is the present value, $r$ is the interest rate per annum and $t$ is the time in years.
\nIn our situation we have,
\n$P=\\$\\var{P}$,
\n$r=\\var{ipa}\\%=\\var{ipadec}$,
\n$t=\\frac{\\var{n}}{\\var{period[1]}}$,
\nand therefore
\n$\\begin{align}S&=\\var{P}\\left(1+\\var{ipadec}\\times \\frac{\\var{n}}{\\var{period[1]}}\\right)\\\\&=\\$ \\var{Srounded} \\text{ (to the nearest cent)}\\end{align}$
", "extensions": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Using simple interest determine the future value, time periods are in days, months, or quarters."}, "ungrouped_variables": ["P", "period", "n", "ipa", "ipadec", "S", "Srounded"], "name": "future value - simple interest", "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "If you are unsure of how to do a question, click on Reveal answers to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again. Do each question repeatedly to ensure you have mastered it.
", "rulesets": {}, "preamble": {"css": "", "js": ""}, "variables": {"Srounded": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "Srounded", "definition": "precround(S,2)"}, "P": {"templateType": "anything", "description": "present value
", "group": "Ungrouped variables", "name": "P", "definition": "random(1000..100000#1000)"}, "n": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "n", "definition": "random(5..40)"}, "period": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "period", "definition": "random(['quarters', 4],['months',12],['days', 365])"}, "ipa": {"templateType": "anything", "description": "interest per annum as a percentage (add the symbol afterwards)
", "group": "Ungrouped variables", "name": "ipa", "definition": "random(3..9#0.01)"}, "S": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "S", "definition": "P*(1+ipadec*n/period[1])"}, "ipadec": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "ipadec", "definition": "ipa/100"}}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}